Martin Bauer

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math.DG2026

Completeness of reparametrization-invariant Sobolev metrics on the space of surfaces

Martin Bauer, Cy Maor, Benedikt Wirth

We study reparametrization-invariant Sobolev-type Riemannian metrics on the space of immersed surfaces and establish conditions ensuring metric and geodesic completeness as well as…

math.DG2025

A Riemannian viewpoint on the Amari-Cencov $I^\pm$ -connections and Proudman-Johnson equations

Martin Bauer, Alice Le Brigant, Cy Maor

We give a new geometric interpretation of the Amari-Cencov $I^\pm$ -connections $\nabla^{(I^\pm)}$ from information geometry: On the space of densities $Dens_{+} (M)$ , we show…

math.DG2024

Completeness and geodesic distance properties for fractional Sobolev metrics on spaces of immersed curves

Martin Bauer, Patrick Heslin, Cy Maor

We investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we consider are Sobolev metrics of poss…

Completeness of reparametrization-invariant Sobolev metrics on the space of surfaces

A Riemannian viewpoint on the Amari-Cencov I^±-connections and Proudman-Johnson equations

Completeness and geodesic distance properties for fractional Sobolev metrics on spaces of immersed curves

A Riemannian viewpoint on the Amari-Cencov $I^\pm$ -connections and Proudman-Johnson equations